1. Field of the Invention
The present invention relates to a scanning force microscope used for studying surface properties of materials on size scales ranging from the angstrom to the micron level.
2. Description of Related Art
Scanning force microscopes (SFM), also referred to as atomic force microscopes (AFM), are known for their use in a broad range of fields where high resolution information regarding the surface region of a sample is desired. Some types of SFMs utilize a small probe comprising a tip attached to the free end of a flexible cantilever for probing the surface of a sample. The tip of the probe is sharp and may either contact the sample or sense the sample without direct contact. The position of the tip is normally determined in all modes of operation of the machine. This position is usually obtained by measuring the angular deflection of the cantilever to which the tip is attached. The cantilever tip assembly is conventionally modeled as a mechanical simple harmonic oscillator (SHO) having an effective mass and effective spring constant.
The length of the cantilever is generally less than 300 xcexcm. Forces between the tip of the probe and the sample surface cause the cantilever to deflect (i.e., bend), and a detector measures the cantilever deflection as the tip is scanned over the sample, or the sample is moved under the tip. The measured cantilever deflections can be used to generate constant force contours that are related to the surface topography. SFMs can be used to study solids, liquids, insulators, semiconductors or electrical conductors.
In addition to imaging, SFMs are used to measure forces of interaction between the probe tip and the surface. This is accomplished by performing a force-distance measurement. Conventional SFMs measure the position of the tip and the position of the sample. The value of a single spring constant associated with the elastic properties of the cantilever is determined experimentally. In a static calibration, the deflection caused by known loads applied to the cantilever is measured, and the constant is obtained from the deflection. In a dynamic calibration, the shift in the lowest resonance frequency of the cantilever is measured for different mass loads, and the constant is derived from that frequency shift. The spring constant is then used to convert cantilever deflections into forces.
The forces that contribute to the deflection of the SFM cantilever can be divided into two categories: repulsive and attractive. The repulsive force that typically dominates at very short range (tip-to-sample separation  less than 0.3 nm) is the strong core repulsive force. At larger separations, the tip-to-sample force arises from a number of physical phenomena such as electrostatics, magneto-statics and surface tension. One important long range force that affects all SFMs is the electrostatic force commonly referred to as the Van Der Waals force. The variation of the total force, including the Van Der Waals force, upon the distance between the tip and the sample depends on whether the distance is within the contact region or the non-contact region. In the contact region, the cantilever is held less than a few tenths of a nano-meter from the sample surface, and the total inter-atomic force between the cantilever and the sample is repulsive. In the non-contact region, the cantilever is held on the order of one to ten nano-meters from the sample surface, and the inter-atomic force between the cantilever and the sample can be either attractive or repulsive. The significance of these two forces can be illustrated with some examples. The repulsive force is responsible for keeping individual elements of systems dispersed, such as keeping red blood cells separate and preventing coagulating of the blood in blood vessels. The attractive force is responsible, for example, for the attachment of drugs to the proper receptors, so that the drugs can have effect.
When used as imaging tools, SFMs operate in one of two modes: variable tip position or constant tip position. In the variable tip position mode, forces between tip and sample are allowed to alter the Z-axis position of the tip. The point at which the tip probes the sample surface is raster scanned (the tip and sample surface move with respect to one another in an X-Y plane) while the position of the tip (along the Z direction) is recorded. In this manner, a series of positional data point sets (x,y,z) are obtained. In the constant tip position mode, the Z position of the tip is maintained fixed during the raster scan, by applying forces to the cantilever through a piezoelectric actuator. In this mode, the Z portion of the positional data point (x,y,z) is obtained by measuring the piezoelectric voltage necessary to maintain a constant separation.
Cantilever based SFMs utilize three distinct sub-modes of operation which can be performed in either the constant tip position mode or the variable tip position mode. These sub-modes are contact, intermittent contact, and non-contact. In contact-SFM, also known as repulsive-SFM, the probe tip makes physical contact with the sample (i.e., the tip is brought close enough to the sample surface so that the dominant repulsive force is the strong core force). The tip is attached to the free end of a cantilever having a spring constant lower than the effective spring constant holding the atoms of the sample together. As the scanner gently traces the tip across the sample (or the sample moves under the tip), the contact force causes the cantilever to bend to accommodate changes in sample topography. The Z position of the cantilever is typically measured using optical techniques. The most common method involves the use of an optic lever, consisting of a laser beam reflected by the surface of the cantilever onto a position-sensitive photo-detector (PSPD). As the cantilever bends, the position of the laser beam on the detector shifts, indicating the bending of the beam, which is approximately equal to the change in the Z-displacement of the free end of the cantilever. Other methods to detect the cantilever deflection are known, and include optical interference, a tunneling microscope, the use of a cantilever fabricated from a piezo-electric material, or a magnetic pickup system.
An SFM can also be operated in a mode where the tip is not in direct contact with the sample surface (i.e., where the dominant force is not the strong core repulsion). The simplest non-contact mode of operation places the tip far enough above the surface so that the structural stiffness of the cantilever at the equilibrium position is sufficient to counter the sum of all attractive forces. The tip-to-sample separation (usually a few nano-meters) must be small enough so that the force field generated by the sample is sufficient to measurably deflect the cantilever. The sample is then moved towards the tip, and the tip displacement is recorded as in the variable contact mode technique. This is the only conventional non-contact mode to work in fluid, but it is difficult to implement.
Another non-contact technique involves oscillating the cantilever near its resonant frequency. The tip-to-sample distance is then reduced until the existence of tip-to-sample forces causes a shift in the resonant frequency of the cantilever. Either the amplitude of vibration at the original resonant frequency is measured or the shift in phase between the driving signal and the cantilever oscillation is measured. A major shortcoming of the oscillating non-contact mode is that it provides lower lateral resolution than the contact mode. Generally, lateral resolution around 10 nano-meters is obtained.
Non-contact SFM is desirable because it provides a means for measuring sample topography with no contact between the tip and the sample and thus causes minimal damage to the sample. It is desirable to have the highest possible resonant frequency so that physically meaningful averages can be taken at reasonable raster scanning rates. Typically, cantilevers with spring constants around 100 N/m having resonant frequencies in the range of 300-600 kHz are utilized. The total force between the tip and the sample in the non-contact region is typically very low, generally about 10xe2x88x9212 N. This low force is advantageous for studying soft or elastic samples as well as non-covalently bound adsorbates on surfaces. A further advantage is that samples like silicon wafers are not contaminated through contact with the tip, conferring an advantage in the microelectronics industry.
Intermittent contact mode is a hybrid of the contact and non-contact modes. In this mode, the cantilever is also made to oscillate near its resonant frequency. The amplitude of oscillation is typically tens to hundreds of nano-meters. A tip-sample separation is chosen so that, at the bottom of its stroke, the probe tip comes into direct contact with the sample surface. Current literature does not describe in detail how the physical interaction between the tip and sample generates the signal measured in intermittent contact mode. In general, it can be said that some combination of the long range force of interaction, the adhesive force, and the strong core repulsion experienced at the bottom of each stroke alters the vibrational amplitude of the cantilever. When operated in air, intermittent contact mode is usually performed with a stiff cantilever like that used in non-contact mode. A benefit of intermittent contact mode is that it reduces lateral dragging of the sample, as compared with contact mode. When scanning in a fluid, lower resonant frequency cantilevers are used (10-100 kHz) to prevent viscous damping forces from extinguishing the signal. An advantage of intermittent contact mode is that it routinely provides very high lateral resolution (almost as high as contact mode) but does not present high shear forces in the X-Y plane. This permits imaging of delicate samples that are easily pushed around by the tip.
In conventional devices, the cantilever-tip assembly is interpreted as a mechanical simple harmonic oscillator (SHO) that cannot vibrate at more than one frequency. In reality, multiple vibrational frequencies are excited during normal SFM operation, and many frequencies exist simultaneously in the system. The linear equation F=xe2x88x92kz (where F is the force, k the spring constant, and z the tip""s deflection measured from its equilibrium position) given by Hooke""s Law for an SHO, does not allow modeling of an oscillator resonating at more than one frequency. As the cantilever approaches the snap-to-contact point (the tip-sample separation where the attractive force gradient exceeds the effective spring constant obtained using the SHO model), the SHO model gives incorrect results. This is because as the cantilever approaches the sample beyond the snap-to-contact point, the cantilever moves fast and cannot oscillate only in its lowest frequency mode. The SHO model thus is not useful in evaluating measurements at and beyond the snap-to-contact point.
The snap to contact point is the point where a large and rapid increase in the attractive force occurs. This increase is analogous to the increase in attractive force experienced when two magnets of opposite polarity are approached. The attractive force gradually increases, up to a point where a further small movement greatly increases the force, and it becomes difficult to keep the poles from contacting.
Conventional devices in which the cantilever is considered to be a simple harmonic oscillator (SHO) also limit the speed with which data can be meaningfully collected. These systems use Hooke""s Law, where the expression F=xe2x88x92kz is used to convert cantilever displacement measurements to tip-sample force values. In these devices, the value of k is assumed to be known, the cantilever vertical deflection z is measured, and thus the force F can be computed. As indicated above, this method is only useful for measurements taken at frequencies lower than the lowest resonant mode of the cantilever. This means that high-speed topographs as well as force-distance measurements taken at high speed are not well modeled using conventional systems.
Static, 3-dimensional measurements of topographic surfaces of materials, such as carbon fiber/polymer composites and semiconductors, can be made using the SHO methods. However, rapid topographical measurements, force-volume images, or real time measurements of interactions of molecules necessary to study biological systems cannot be done reliably using an SHO model, because they require very rapid measurements.
Another problem with conventional devices is that the speed at which the cantilever approaches the sample must be slow enough so that the cantilever does not vibrate above its first mode. If the speed of motion of the cantilever is above a certain value, then vibrations will be induced in the cantilever, and the measurements of the force will give inaccurate readings of the tip-to-sample distance (d). Conventional methods can provide only one data point (tip-to-sample distance) each millisecond, and thus cannot scan a surface topography of an area fast enough for real-time imaging of a biological living sample, such as a protein, which can move many pixels in one second and change the topography of the area during the scan. To have chemical specificity while resolving the motion of such a biological living sample, meaning that the chemical composition of the sample can be determined, one needs to get force-distance measurements at each pixel consisting of several measurements at each location on the X-Y plane. Thus, even for a modestly sized 64xc3x9764xc3x9764 points image, the frequency of the cantilever must be larger than 105 voxels/sec. Under those conditions, vibrational modes having frequencies larger than the lowest natural frequency of the cantilever will be excited.
In light of the foregoing, there is a need in the art for an improved SFM.
Accordingly, the present invention is directed to a method and device that substantially obviate one or more limitations of the related art. To achieve these and other advantages, and in accordance with the purposes of the invention, as embodied and broadly described herein, the invention involves a method for determining a force of interaction between a sample and a tip on a cantilever. The method includes positioning the sample and the cantilever tip a predetermined distance from each other, rapidly measuring respective positions of a plurality of points on the cantilever as the cantilever is deflected by the force of interaction, modeling the cantilever with a non-Hookian model that accounts for higher order vibrational modes of the cantilever, and calculating the force of interaction from the measured positions of the plurality of points using the model.
Another aspect of the invention includes a method for determining a force-distance curve for an interaction between a tip on a cantilever and a sample. The force-distance curve is determined by positioning the sample and the cantilever tip a predetermined distance from each other, rapidly measuring the respective positions of a plurality of points on the cantilever as the cantilever is deflected by the force of interaction, modeling the interaction with a non-Hookian model that accounts for higher order vibrational modes of the cantilever for the predetermined distance, calculating the force of interaction from the measured positions of the plurality of points using the model thus determining one point of the force-distance curve, varying the predetermined distance by a preselected distance increment, and repeating the rapidly measuring, the modeling, the calculating, and the varying of a preselected number of times until the force-distance curve is determined.
In yet another aspect, the invention includes an apparatus for determining a force of interaction between a sample and a tip on a cantilever. The apparatus comprises a positioning mechanism to position the tip at a known location in relation to the sample, a deflection measurer for determining rapidly the deflection due to the force of interaction of a plurality of points on the cantilever, a processor for modeling the cantilever with a non-Hookian model accounting for higher order vibrational modes of the cantilever, and for calculating the force of interaction from the measured deflection of the plurality of points using the model of the cantilever, a memory for storing instructions for the processor to model the cantilever, and a controller for directing the positioning mechanism to position the tip at predetermined locations.
The present invention preferably obtains accurate force measurements using an SFM at high speed. This invention allows the distance between the cantilever tip and the sample to be changed rapidly at an exact point (or xe2x80x9cpixelxe2x80x9d) that is being probed over the sample, and also allows rapid movement of the tip across the sample, in a xe2x80x9craster-scanningxe2x80x9d movement to analyze the entire surface of the sample. There are two specific situations in which this accuracy at high speed is desired. First, when the tip-to-sample separation is very small (within the snap-to-contact region). Second, when high data collection rates are desired for high-speed imaging and/or high speed force-distance measurements, as required when analyzing chemical or biological systems.
These accurate high speed force measurements are accomplished by a system utilizing a non-linear equation to model the resonant frequencies of the cantilever used to measure the tip-to-sample interaction. This system interprets accurately the higher order resonance modes of the cantilever that are excited in high speed applications. The method of the present invention does not necessarily require exact knowledge of the shape of the cantilever in order to obtain measured forces. Thus, it can be applied to existing SFM technology.
More specifically, the present invention allows for a direct spatial analysis of the data retrieved from scanning force microscopes working at high frequencies. Instead of determining the force of interaction between the cantilever tip and the sample by measuring the deflection of one location on the cantilever over time, the system of this invention measures cantilever deflection for a snapshot in time, at different locations on the cantilever. These rapid measurements of the deflection at multiple points are used in the model to obtain the force of interaction at a specific distance and location of the tip over the sample. The measurements are taken rapidly so that the cantilever does not substantially move between measurements of successive points.
For example, a modulated laser beam can measure the deflection of several points on the cantilever rapidly. Alternatively, more than one laser beam may be used, one measuring the deflection of each different point. Other suitable known methods for rapidly measuring the deflection of the cantilever at several locations can be used.
The force of interaction between the cantilever tip and the sample is thus determined according to the invention by applying a non-Hookian equation to data describing the deflection of points of the cantilever at one instant in time. In a preferred embodiment, the sample is moved toward and away from the cantilever, and the force computation according to the invention is repeated at several known distances between the sample and the cantilever. A force-separation curve can then be constructed, describing how the force of interaction changes as the tip is moved toward/away from the sample, over a specific X-Y location of the sample.
The force-separation curve is expected to have a characteristic shape for specific chemical elements. If the curve is compared to a library of curves from known elements and chemical compounds, the composition of the sample at the point being analyzed could be determined to obtain information about the distribution of elements within the sample on a molecular scale. However, at the present time a quantitative cataloguing of curves has not been developed, and the measurements could only be evaluated qualitatively.
In another embodiment according to the invention, the entire sample may be raster-scanned by the tip of the cantilever, so that force-distance curves can be constructed at successive locations over the sample, to produce an image of the entire sample that includes the sample""s chemical composition. The raster-scan can be repeated to produce successive images showing the development over time of the sample, if the scanning is performed fast enough.
These applications are possible due to the ability of the system according to the present invention to interpret the higher oscillation modes of the cantilever that are excited when the cantilever is moved very rapidly toward the sample, and is moved from one position to the next on the sample at high speed. The system according to the present invention preferably only requires measurements of cantilever deflection at one instant in time at each distance between the sample and the cantilever. In the preferred embodiment, the force-separation curve can be generated more rapidly in this manner than is possible in systems requiring several measurements in time for each discrete distance.
Information regarding dynamic systems, such as cells and other biological samples, can also be determined by the system of the invention, before the sample has time to change. The ability of the system to interpret the higher vibrational modes of the cantilever that are excited during fast operation permits completing a raster scan of the entire sample before the sample changes substantially.
Besides the arrangements set forth below, the invention could include a number of other arrangements, such as those explained hereinafter. It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the invention as claimed.